On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

Acceleration of the Cosmological Expansion as an Effect of Inhomogeneities

The cosmological observations of light from type Ia supernovae, the cosmic microwave background and the galaxy distribution seem to indicate that the expansion of the universe has accelerated during the latter half of its age. Within standard cosmology, this is ascribed to dark energy, a uniform fluid with large negative pressure that gives rise to repulsive gravity but also entails serious theoretical problems. Understanding the physical origin of the perceived accelerated expansion has been described as one of the greatest challenges in theoretical physics today. In this thesis, we discuss the possibility that, instead of dark energy, the acceleration would be caused by an effect of the nonlinear structure formation on light, ignored in the standard cosmology. A physical interpretation of the effect goes as follows: due to the clustering of the initially smooth matter with time as filaments of opaque galaxies, the regions where the detectable light travels get emptier and emptier relative to the average. As the developing voids begin to expand the faster the lower their matter density becomes, the expansion can then accelerate along our line of sight without local acceleration, potentially obviating the need for the mysterious dark energy. In addition to offering a natural physical interpretation to the acceleration, we have further shown that an inhomogeneous model is able to match the main cosmological observations without dark energy, resulting in a concordant picture of the universe with 90% dark matter, 10% baryonic matter and 15 billion years as the age of the universe. The model also provides a smart solution to the coincidence problem: if induced by the voids, the onset of the perceived acceleration naturally coincides with the formation of the voids. Additional future tests include quantitative predictions for angular deviations and a theoretical derivation of the model to reduce the required phenomenology. A spin-off of the research is a physical classification of the cosmic inhomogeneities according to how they could induce accelerated expansion along our line of sight. We have identified three physically distinct mechanisms: global acceleration due to spatial variations in the expansion rate, faster local expansion rate due to a large local void and biased light propagation through voids that expand faster than the average. A general conclusion is that the physical properties crucial to account for the perceived acceleration are the growth of the inhomogeneities and the inhomogeneities in the expansion rate. The existence of these properties in the real universe is supported by both observational data and theoretical calculations. However, better data and more sophisticated theoretical models are required to vindicate or disprove the conjecture that the inhomogeneities are responsible for the acceleration.

What should I think; How should I feel? : The balancing of personal experiences and social norms in the outgroup attitude formation of youth

The present study focused on the associations between the personal experiences of intergroup contact, perceived social norms and the outgroup attitudes of Finnish majority and Russian-speaking minority youth living in Finland. The theoretical background of the study was derived from Allport s (1954) theory of intergroup contact (i.e., the contact hypothesis), social psychological research on normative influences on outgroup attitudes (e.g., Rutland, 2004; Stangor and Leary, 2006) and developmental psychological research on the formation of explicit (deliberate) and implicit (automatically activated) outgroup attitudes in adolescence (e.g., Barrett, 2007; Killen, McGlothlin and Henning, 2008). The main objective of the study was to shed light on the role of perceived social norms in the formation of outgroup attitudes among adolescents. First, the study showed that perceived normative pressure to hold positive attitudes towards immigrants regulated the relationship between the explicit and implicit expression of outgroup attitudes among majority youth. Second, perceived social norms concerning outgroup attitudes (i.e., the perceived outgroup attitudes of parents and peers) affected the relationship between intergroup contact and explicit outgroup attitudes depending on gender and group status. Positive social norms seem to be especially important for majority boys, who need both pleasant contact experiences and normative support to develop outgroup attitudes that are as positive as girls attitudes. The role of social norms is accentuated also among minority youth, who, contrary to majority youth with their more powerful and independent status position, need to reflect upon their attitudes and experiences of negative intergroup encounters in relation to the experiences and attitudes of their ingroup members. Third, the results are indicative of the independent effects of social norms and intergroup anxiety on outgroup attitudes: the effect of perceived social norms on the outgroup attitudes of youth seems to be at least as strong as the effect of intergroup anxiety. Finally, it was shown that youth evaluate intergroup contact from the viewpoint of their ingroup and society as a whole, not just based on their own experiences. In conclusion, the outgroup attitudes of youth are formed in a close relationship with their social environment. On the basis of this study, the importance of perceived social norms for research on intergroup contact effects among youth cannot be overlooked. Positive normative influences have the potential to break the strong link between rare and/or negative personal contact experiences and negative outgroup attitudes, and norms also influence the relationship between implicit and explicit attitude expression.

Conflits de norms de justice distributive dans les fusions entre égaux Le cas de BioM.rieux-Pierre Fabre

Les strictes fusions entre égaux constituent un phénomène très rare. Pourtant, de nombreux dirigeants communiquent sur l’aspect égalitaire des fusions et acquisitions qu’ils conçoivent. Dans cet article, les auteurs expliquent pourquoi les dirigeants <> leurs F&A en <> ; montrent en quoi le postulat égalitaire initial accroît la probabilité de conflits entre deux normes de justice distributive pourtant compl.mentaires : l’égalité et l’équité ; et illustrent leurs propos avec un cas spectaculaire : la fusion égalitaire, puis la separation des entreprises BioMérieux et Pierre Fabre. Paradoxalement, la simple formulation en termes égalitaire des F&A favorise la diffusion de sentiments d’injustice distributive, qui nuit in fine à la performance de l’opération.

Looking-Glass Reflections : Norms in translating Lewis Carroll

This thesis in the field of translation studies focusses on the role of norms in the work of a literary translator. Norms are seen as guidelines for the translator; they also reflect the way the target audience either accepts or rejects the translation. Thus they are of an intersubjective nature. The theoretical background of the study is based on the views on norms of Andrew Chesterman and Gideon Toury. The writer makes use of her own editing and publishing experience, as well as her experience in translating Lewis Carroll, considering these in respect to theoretical views of norms and vice versa. The aim is also to bring to light some of the tacit knowledge related to translating, editing and publishing in Finland. The study has three angles. First, the writer introduces the norms of Finnish literary translation as gathered from her own working experience. The sources from which these norms arise and which affect them are briefly described. Six central translation norms emerge; they are described and exemplified through cases of Carroll translation. Secondly, a small-scale questionnaire study is presented. This was carried out in order to sound the normative views of other translators and to limit the role of subjectivity. The views of the informants largely support the set of norms presented by the writer, although the norms of quotability and harmony between translation and illustration do not arise. Instead, the answers give rise to a seventh, ethical norm, which is labelled the norm of integrity. Thirdly, there is a brief presentation of Lewis Carroll, his Alice books and their translation history in Finland. The retranslation hypothesis and the motives of retranslation are considered in the light of the work of Outi Paloposki and Kaisa Koskinen. The final part of the thesis plunges into actual translation work. It includes one and a half chapters of Through the Looking-Glass (Alicen seikkailut peilintakamaassa) as translated into Finnish by the writer. The translation commentary first discusses a number of recurring and general translation points; the running commentary then analyses 77 individual translation solutions and their justifications. The writer uses introspection as a way of reflecting on her own translation process, its decisive points and the role of norms therein. Keywords: Translation studies, Carroll, norms